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Transient analysis of state-dependent queueing networks via cumulant functions

Part of: Probabilistic methods, simulation and stochastic differential equations Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Timothy I. Matis  and
Richard M. Feldman
Timothy I. Matis*
Affiliation:
New Mexico State University
Richard M. Feldman*
Affiliation:
Texas A & M University
*
∗ Postal address: Department of Industrial Engineering, New Mexico State University, Las Cruces, NM 88003-8001, USA.
∗∗ Postal address: Department of Industrial Engineering, Texas A & M University, College Station, TX 77843-3131, USA. Email address: richf@tamu.edu
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Abstract

A new procedure that generates the transient solution of the first moment of the state of a Markovian queueing network with state-dependent arrivals, services, and routeing is developed. The procedure involves defining a partial differential equation that relates an approximate multivariate cumulant generating function to the intensity functions of the network. The partial differential equation then yields a set of ordinary differential equations which are numerically solved to obtain the first moment.

Keywords

Queuesqueueing networkscumulant generating functionstransient solutions

MSC classification

Primary: 90B22: Queues and service 60K25: Queueing theory 90B15: Network models, stochastic 65C99: None of the above, but in this section 90B99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 841 - 859
Copyright
Copyright © by the Applied Probability Trust 2001 

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